Finite Group Databasebeta

← C5×#73006 #14510730

Subgroups — C5×#73006 #14510730

Order 1920.

228 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#399⋊C3C211yesmaximal, characteristic, complemented
2C5×#4622C211yesmaximal, characteristic, complemented
3C5×#4621C211yesmaximal, characteristic, complemented
4C5×#1618—31nomaximal, Hall
5C5×GL(2,ℤ/4)—41nomaximal
6C5×#95⋊C3C2211yescharacteristic
7#73006C511yesmaximal, characteristic, direct product factor, Hall
8C5×#538—31no—
9C5×#484—31no—
10C5×#481—31no—
11C5×#399D311yescharacteristic, complemented
12C5×#328—31no—
13C5×#327—31no—
14C5×#323—31no—
15C22×C5×A4—41no—
16C2×C5×S4—41no—
17C5×SL(2,ℤ/4)—41no—
18#399⋊C3C2×C511yescharacteristic, complemented
19#4622C2×C511yescharacteristic, complemented
20#4621C2×C511yescharacteristic, complemented
21C5×#126—61no—
22C5×#124—61no—
23C5×#123—61no—
24C5×C22⋊Q8—31no—
25C5×#121—31no—
26C5×#121—61no—
27C5×#120—61no—
28C4×C5×D4—61no—
29C2×C5×C4⋊C4—31no—
30C2×C5×C22⋊C4—31no—
31C5×#107—61no—
32C5×#106—61no—
33C5×#103—61no—
34C5×#102—61no—
35C5×C22⋊C8—31no—
36C5×C22⋊C8—31no—
37C5×#95C2×D311yescharacteristic
38#1618—31noSylow
39C2×C5×A4—41no—
40C2×C5×A4—81no—
41C5×S4—81no—
42C5×#67—161no—
43GL(2,ℤ/4)—41no—
44#95⋊C3C22×C511yescharacteristic
45C24×C5S411yescharacteristic
46C2×C5×Q8—31no—
47C2×C5×D4—31no—
48C2×C5×D4—61no—
49C2×C5×D4—61no—
50C2×C5×D4—61no—
51C22×C4×C5—31no—
52C22×C4×C5—31no—
53C22×C4×C5—61no—
54C2×C5×C8—61no—
55C2×C5×C8—61no—
56C5×C4⋊C4—31no—
57C5×C4⋊C4—31no—
58C5×C4⋊C4—61no—
59C5×C4⋊C4—61no—
60C5×C4⋊C4—61no—
61C5×C4⋊C4—61no—
62C5×C22⋊C4—61no—
63C5×C22⋊C4—61no—
64C5×C22⋊C4—61no—
65C5×C22⋊C4—61no—
66C5×C22⋊C4—61no—
67C5×C22⋊C4—61no—
68C5×C22⋊C4—61no—
69C42×C5—61no—
70#538—31no—
71#484—31no—
72#481—31no—
73#399C5×D311yescharacteristic, complemented
74#328—31no—
75#327—31no—
76#323—31no—
77C22×C3×C5—161no—
78C2×C5×D3—161no—
79C5×A4—41no—
80C5×Dic3—161no—
81C22×A4—41no—
82C2×S4—41no—
83SL(2,ℤ/4)—41no—
84C23×C5—21no—
85C23×C5—61no—
86C23×C5—61no—
87C23×C5—61no—
88C23×C5C2×S411yescharacteristic
89C5×Q8—121no—
90C5×D4—121no—
91C5×D4—121no—
92C5×D4—121no—
93C5×D4—241no—
94C5×D4—241no—
95C2×C4×C5—31no—
96C2×C4×C5—31no—
97C2×C4×C5—61no—
98C2×C4×C5—61no—
99C2×C4×C5—61no—
100C2×C4×C5—61no—
101C2×C4×C5—121no—
102C2×C4×C5—121no—
103C2×C4×C5—241no—
104C5×C8—121no—
105C5×C8—121no—
106#126—61no—
107#124—61no—
108#123—61no—
109C22⋊Q8—31no—
110#121—31no—
111#121—61no—
112#120—61no—
113C4×D4—61no—
114C2×C4⋊C4—31no—
115C2×C22⋊C4—31no—
116#107—61no—
117#106—61no—
118#103—61no—
119#102—61no—
120C22⋊C8—31no—
121C22⋊C8—31no—
122#95C2×C5×D311yescharacteristic
123C2×C3×C5—161no—
124C2×C3×C5—321no—
125C5×D3—321no—
126C2×A4—41no—
127C2×A4—81no—
128S4—81no—
129#67—161no—
130C22×C5—31no—
131C22×C5—31no—
132C22×C5—41no—
133C22×C5—121no—
134C22×C5—121no—
135C22×C5—121no—
136C22×C5—121no—
137C22×C5—121no—
138C22×C5#98311yescharacteristic
139C4×C5—61no—
140C4×C5—61no—
141C4×C5—121no—
142C4×C5—121no—
143C4×C5—121no—
144C4×C5—121no—
145C24C5×S411yescharacteristic
146C2×Q8—31no—
147C2×D4—31no—
148C2×D4—61no—
149C2×D4—61no—
150C2×D4—61no—
151C22×C4—31no—
152C22×C4—31no—
153C22×C4—61no—
154C2×C8—61no—
155C2×C8—61no—
156C4⋊C4—31no—
157C4⋊C4—31no—
158C4⋊C4—61no—
159C4⋊C4—61no—
160C4⋊C4—61no—
161C4⋊C4—61no—
162C22⋊C4—61no—
163C22⋊C4—61no—
164C22⋊C4—61no—
165C22⋊C4—61no—
166C22⋊C4—61no—
167C22⋊C4—61no—
168C22⋊C4—61no—
169C42—61no—
170C3×C5—161noHall
171C22×C3—161no—
172C2×D3—161no—
173A4—41no—
174Dic3—161no—
175C2×C5—31no—
176C2×C5—31no—
177C2×C5—81no—
178C2×C5—241no—
179C2×C5#857⋊C211yescharacteristic
180C23—21no—
181C23—61no—
182C23—61no—
183C23—61no—
184C23C2×C5×S411yescharacteristic
185Q8—121no—
186D4—121no—
187D4—121no—
188D4—121no—
189D4—241no—
190D4—241no—
191C2×C4—31no—
192C2×C4—31no—
193C2×C4—61no—
194C2×C4—61no—
195C2×C4—61no—
196C2×C4—61no—
197C2×C4—121no—
198C2×C4—121no—
199C2×C4—241no—
200C8—121no—
201C8—121no—
202C2×C3—161no—
203C2×C3—321no—
204D3—321no—
205C5#7300611yescharacteristic, direct product factor, Sylow
206C22—31no—
207C22—31no—
208C22—41no—
209C22—121no—
210C22—121no—
211C22—121no—
212C22—121no—
213C22—121no—
214C22C5×#98311yescharacteristic
215C4—61no—
216C4—61no—
217C4—121no—
218C4—121no—
219C4—121no—
220C4—121no—
221C3—161noSylow
222C2—31no—
223C2—31no—
224C2—81no—
225C2—241no—
226C2C5×#857⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2×C5#857⋊C2
commutator, cosocle, hypocenter#95⋊C3C22×C5
FrattiniC23C2×C5×S4
FittingC5×#399D3
socleC23×C5C2×S4
LCSG ▷ #95⋊C3
UCSC1 ◁ C2×C5

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#399⋊C3C2semidirect
2. C5×#4622C2semidirect
3. C5×#4621C2semidirect
7. #73006C5direct (N × H)
11. C5×#399D3semidirect
18. #399⋊C3C2×C5semidirect
19. #4622C2×C5semidirect
20. #4621C2×C5semidirect
73. #399C5×D3semidirect
205. C5#73006direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#399⋊C32
C5×#46222
C5×#46212
C5×#16183
C5×GL(2,ℤ/4)4
#730065